Vintage :

Amiga Boing Ball - http://www.youtube.com/watch?v=-ga41edXw3A
Making of the Amiga Boing Ball - http://www.youtube.com/watch?v=cJcO628yCcU

Amiga Juggler & Cat - http://www.youtube.com/watch?v=g03rcG7F4PU

Who could forget? <3 Those were iconic!

I couldn't find it at the time of posting, but here's one I think you'll appreciate. It's from a little later on, 1995, but still impresses me for the poor ol' 'miga. :'D
http://www.youtube.com/watch?v=xFO7bWcCRCA

Oh God! Spaceballs' STATE OF THE ART!! -- http://www.youtube.com/watch?v=L0WUoOcxRl0
A basic Amiga 500 and an 880K floppy were the only things necessary to run it. That demo impressed the living snot out of me. I'd seen a few other demos, but none were as memorable to me as that one.

I couldn't find it at the time, but here's one that really impressed me from a little later in 1995.
http://www.youtube.com/watch?v=xFO7bWcCRCA

Also, if that's your thing, here's a freakin' amazing one from 2011;
http://www.youtube.com/watch?v=8MMwO8Mvqfs

That latter is seizure inducing.

I haven't seen much demo since the A4000 went tits up, Still love my old Amigas but the production machine is Linux.